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The relationship between Stress-Energy tensor and Mass

  1. Dec 9, 2012 #1

    ShayanJ

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    In Einstein field equations,the term that is responsible for curving Space-Time is the Stress-Energy tensor.But we know that mass should be able to curve space-time.So I think every mass distribution should have a Stress-Energy tensor associated with it.
    What is that relationship?
    Thanks
     
  2. jcsd
  3. Dec 9, 2012 #2

    dextercioby

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    Volumic mass density is the 00 component of the stress-energy tensor.
     
  4. Dec 9, 2012 #3

    stevendaryl

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    The relationship is explained in Wikipedia here: http://en.wikipedia.org/wiki/Stress–energy_tensor

    The simplest case is a perfect fluid at rest. In that case, the nonzero components of the stress-energy tensor [itex]T^{\alpha \beta}[/itex] are:
    [itex]T^{0 0} = \rho[/itex], where [itex]rho[/itex] is the mass-energy density, and
    [itex]T^{1 1} = T^{2 2} = T^{3 3} = p[/itex], where [itex]p[/itex] is the pressure.
     
  5. Dec 9, 2012 #4

    K^2

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    Energy density, which is proportional to mass density only for a body at rest.
     
  6. Dec 9, 2012 #5

    ShayanJ

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    Thanks guys
    But what about other components?
     
  7. Dec 12, 2012 #6

    stevendaryl

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    As I said, for a fluid at rest, the three spatial components of the stress-energy tensor are just the pressure.
     
  8. Dec 12, 2012 #7

    jtbell

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    The diagram on the Wikipedia page identifies what the various components (or groups of them) represent.
     
  9. Dec 12, 2012 #8
    In addition to what Steven said, the off diagonal terms are shear stresses.
     
  10. Dec 12, 2012 #9

    pervect

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    And of course you have momentum density....if you have a moving object or fluid.
     
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